Lines on one-parameter calabi-yau hypersurfaces

In this thesis, we investigate the behavior of families of lines on one-parameter projective hypersurfaces via the inhomogeneous Picard-Fuchs equation satisfied by the normal functions of the corresponding algebraic cycles. Since the algebraic cycles are geometric invariants, their monodromies aroun...

Full description

Bibliographic Details
Main Author: Jefferson, Robert
Other Authors: Johannes Walcher (Internal/Supervisor)
Format: Others
Language:en
Published: McGill University 2013
Subjects:
Online Access:http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=119712
id ndltd-LACETR-oai-collectionscanada.gc.ca-QMM.119712
record_format oai_dc
spelling ndltd-LACETR-oai-collectionscanada.gc.ca-QMM.1197122014-02-13T04:12:04ZLines on one-parameter calabi-yau hypersurfacesJefferson, RobertPhysics - TheoryIn this thesis, we investigate the behavior of families of lines on one-parameter projective hypersurfaces via the inhomogeneous Picard-Fuchs equation satisfied by the normal functions of the corresponding algebraic cycles. Since the algebraic cycles are geometric invariants, their monodromies around singular loci in the complex structure moduli space provide information about the physics of the underlying variety, i.e. of Calabi-Yau manifolds. In particular, such cycles contribute to the calculation of the D-brane superpotential, with an associated mirror symmetry interpretation. Relations to number theory also arise, as the critical values of the superpotential are found to belong to field extensions of the rationals. Additionally, the contribution to the superpotential may have relevance for the scalar supergravity potential, and hence for the landscape of flux vacua and string phenomenology, which serves as further physics motivation for our study.Dans cette these, on examine le comportement de familles de droites sur des hypersurfaces projectives a un parametre en passant par l'equation de Picard-Fuchs inhomogene satisfaite par les fonctions normales de cycles algebriques correspondants. Etant donne que les cycles algebriques sont des invariants geometriques, leur monodromie autour des points singuliers dans l'espace des modules de la structure complexe fournit de l'information sur les proprietes physique de la variete sous-jacente, qui est de Calabi-Yau. Notamment, de tels cycles contribuent a l'evaluation du super-potentiel de D-branes, ayant une interpretation en symetrie miroir associee. On trouve egalement des liens avec la theorie des nombres, car les valeurs critiques du superpotentiel se trouvent appartenir a des extensions de corps des nombres rationnels. De plus, la contribution au superpotentiel pourrait s'averer important pour le potentiel scalaire de supergravite, et ainsi pour le paysage des vides de flux et la phenomenologie des cordes, qui est une source de motivation supplementaire pour poursuivre cette etude.McGill UniversityJohannes Walcher (Internal/Supervisor)2013Electronic Thesis or Dissertationapplication/pdfenElectronically-submitted theses.All items in eScholarship@McGill are protected by copyright with all rights reserved unless otherwise indicated.Master of Science (Department of Physics) http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=119712
collection NDLTD
language en
format Others
sources NDLTD
topic Physics - Theory
spellingShingle Physics - Theory
Jefferson, Robert
Lines on one-parameter calabi-yau hypersurfaces
description In this thesis, we investigate the behavior of families of lines on one-parameter projective hypersurfaces via the inhomogeneous Picard-Fuchs equation satisfied by the normal functions of the corresponding algebraic cycles. Since the algebraic cycles are geometric invariants, their monodromies around singular loci in the complex structure moduli space provide information about the physics of the underlying variety, i.e. of Calabi-Yau manifolds. In particular, such cycles contribute to the calculation of the D-brane superpotential, with an associated mirror symmetry interpretation. Relations to number theory also arise, as the critical values of the superpotential are found to belong to field extensions of the rationals. Additionally, the contribution to the superpotential may have relevance for the scalar supergravity potential, and hence for the landscape of flux vacua and string phenomenology, which serves as further physics motivation for our study. === Dans cette these, on examine le comportement de familles de droites sur des hypersurfaces projectives a un parametre en passant par l'equation de Picard-Fuchs inhomogene satisfaite par les fonctions normales de cycles algebriques correspondants. Etant donne que les cycles algebriques sont des invariants geometriques, leur monodromie autour des points singuliers dans l'espace des modules de la structure complexe fournit de l'information sur les proprietes physique de la variete sous-jacente, qui est de Calabi-Yau. Notamment, de tels cycles contribuent a l'evaluation du super-potentiel de D-branes, ayant une interpretation en symetrie miroir associee. On trouve egalement des liens avec la theorie des nombres, car les valeurs critiques du superpotentiel se trouvent appartenir a des extensions de corps des nombres rationnels. De plus, la contribution au superpotentiel pourrait s'averer important pour le potentiel scalaire de supergravite, et ainsi pour le paysage des vides de flux et la phenomenologie des cordes, qui est une source de motivation supplementaire pour poursuivre cette etude.
author2 Johannes Walcher (Internal/Supervisor)
author_facet Johannes Walcher (Internal/Supervisor)
Jefferson, Robert
author Jefferson, Robert
author_sort Jefferson, Robert
title Lines on one-parameter calabi-yau hypersurfaces
title_short Lines on one-parameter calabi-yau hypersurfaces
title_full Lines on one-parameter calabi-yau hypersurfaces
title_fullStr Lines on one-parameter calabi-yau hypersurfaces
title_full_unstemmed Lines on one-parameter calabi-yau hypersurfaces
title_sort lines on one-parameter calabi-yau hypersurfaces
publisher McGill University
publishDate 2013
url http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=119712
work_keys_str_mv AT jeffersonrobert linesononeparametercalabiyauhypersurfaces
_version_ 1716647387328413696